Online Nonnegative Matrix Factorization with Outliers
R. Zhao, und V. Tan. (2016)cite arxiv:1604.02634v1.pdf.
Zusammenfassung
We propose a unified and systematic framework for performing online
nonnegative matrix factorization in the presence of outliers that is
particularly suited to large datasets. Within this framework, we propose two
solvers based on proximal gradient descent and alternating direction method of
multipliers. We prove that the objective function converges almost surely by
appealing to the quasi-martingale convergence theorem. We also show the learned
basis matrix converges to the set of local minimizers of the objective function
almost surely. In addition, we extend our basic problem formulation to various
settings with different constraints and regularizers, and adapt the solvers and
analyses to each setting. We perform extensive experiments on both synthetic
and image datasets. These experiments demonstrate the efficiency and efficacy
of our algorithm on tasks such as basis learning, image denoising and shadow
removal.
%0 Generic
%1 zhao2016online
%A Zhao, Renbo
%A Tan, Vincent Y. F.
%D 2016
%K nmf
%T Online Nonnegative Matrix Factorization with Outliers
%U http://arxiv.org/abs/1604.02634
%X We propose a unified and systematic framework for performing online
nonnegative matrix factorization in the presence of outliers that is
particularly suited to large datasets. Within this framework, we propose two
solvers based on proximal gradient descent and alternating direction method of
multipliers. We prove that the objective function converges almost surely by
appealing to the quasi-martingale convergence theorem. We also show the learned
basis matrix converges to the set of local minimizers of the objective function
almost surely. In addition, we extend our basic problem formulation to various
settings with different constraints and regularizers, and adapt the solvers and
analyses to each setting. We perform extensive experiments on both synthetic
and image datasets. These experiments demonstrate the efficiency and efficacy
of our algorithm on tasks such as basis learning, image denoising and shadow
removal.
@misc{zhao2016online,
abstract = {We propose a unified and systematic framework for performing online
nonnegative matrix factorization in the presence of outliers that is
particularly suited to large datasets. Within this framework, we propose two
solvers based on proximal gradient descent and alternating direction method of
multipliers. We prove that the objective function converges almost surely by
appealing to the quasi-martingale convergence theorem. We also show the learned
basis matrix converges to the set of local minimizers of the objective function
almost surely. In addition, we extend our basic problem formulation to various
settings with different constraints and regularizers, and adapt the solvers and
analyses to each setting. We perform extensive experiments on both synthetic
and image datasets. These experiments demonstrate the efficiency and efficacy
of our algorithm on tasks such as basis learning, image denoising and shadow
removal.},
added-at = {2021-02-08T15:15:18.000+0100},
author = {Zhao, Renbo and Tan, Vincent Y. F.},
biburl = {https://www.bibsonomy.org/bibtex/22df8dd5e752ae1ae87342eb2958e1473/bsc},
description = {1604.02634v1.pdf},
interhash = {e6bf476767cbf5d83692928e67c66374},
intrahash = {2df8dd5e752ae1ae87342eb2958e1473},
keywords = {nmf},
note = {cite arxiv:1604.02634v1.pdf},
timestamp = {2021-02-08T15:15:18.000+0100},
title = {Online Nonnegative Matrix Factorization with Outliers},
url = {http://arxiv.org/abs/1604.02634},
year = 2016
}